Invisibility and indistinguishability in structural damage tomography

Structural damage tomography (SDT) uses full-field or distributed measurements collected from sensors or self-sensing materials to reconstruct quantitative images of potential damage in structures, such as civil structures, automobiles, aircraft, etc. In approximately the past ten years, SDT has increased in popularity due to significant gains in computing power, improvements in sensor quality, and increases in measurement device sensitivity. Nonetheless, from a mathematical standpoint, SDT remains challenging because the reconstruction problems are usually nonlinear and ill-posed. Inasmuch, the ability to reliably reconstruct or detect damage using SDT is seldom guaranteed due to factors such as noise, modeling errors, low sensor quality, and more. As such, damage processes may be rendered invisible due to data indistinguishability. In this paper we identify and address key physical, mathematical, and practical factors that may result in invisible structural damage. Demonstrations of damage invisibility and data indistinguishability in SDT are provided using experimental data generated from a damaged reinforced concrete beam

A multiscale modelling approach for estimating the effect of defects in unidirectional carbon fiber reinforced polymer composites

A multiscale modelling approach was developed in order to estimate the effect of defects on the strength of unidirectional carbon fiber composites. The work encompasses a micromechanics approach, where the known reinforcement and matrix properties are experimentally verified and a 3D finite element model is meshed directly from micrographs. Boundary conditions for loading the micromechanical model are derived from macroscale finite element simulations of the component in question. Using a microscale model based on the actual microstructure, material parameters and load case allows realistic estimation of the effect of a defect. The modelling approach was tested with a unidirectional carbon fiber composite beam, from which the micromechanical model was created and experimentally validated. The effect of porosity was simulated using a resin-rich area in the microstructure and the results were compared to experimental work on samples containing pores

Less is often more : applied inverse problems using hp-forward models

To solve an applied inverse problem, a numerical forward model for the problem’s physics is required. Commonly, the finite element method is employed with discretizations consisting of elements with variable size h and polynomial degree p. Solutions to hp-forward models are known to converge exponentially by simultaneously decreasing h and increasing p. On the other hand, applied inverse problems are often ill-posed and their minimization rate exhibits uncertainty. Presently, the behavior of applied inverse problems incorporating hp elements of differing p, h, and geometry is not fully understood. Nonetheless, recent research suggests that employing increasingly higher-order hp-forward models (increasing mesh density and p) decreases reconstruction errors compared to inverse regimes using lower-order hp-forward models (coarser meshes and lower p). However, an affirmative or negative answer to following question has not been provided, “Does the use of higher order hp-forward models in applied inverse problems always result in lower error reconstructions than approaches using lower order hp-forward models?” In this article we aim to reduce the current knowledge gap and answer the open question by conducting extensive numerical investigations in the context of two contemporary applied inverse problems: elasticity imaging and hydraulic tomography – nonlinear inverse problems with a PDE describing the underlying physics. Our results support a negative answer to the question – i.e. decreasing h (increasing mesh density), increasing p, or simultaneously decreasing h and increasing p does not guarantee lower error reconstructions in applied inverse problems. Rather, there is complex balance between the accuracy of the hp-forward model, noise, prior knowledge (regularization), Jacobian accuracy, and ill-conditioning of the Jacobian matrix which ultimately contribute to reconstruction errors. As demonstrated herein, it is often more advantageous to use lower-order hp-forward models than higherorder hp-forward models in applied inverse problems. These realizations and other counterintuitive behavior of applied inverse problems using hp-forward models are described in detail herein

Modeling water absorption in concrete and mortar with distributed damage

The deterioration rate of concrete structures is directly influenced by the rate of moisture ingress. Modeling moisture ingress in concrete is therefore essential for quantitative estimation of the service life of concrete structures. While models for saturated moisture transport are commonly used, concrete, during its service life, is rarely saturated and some degree of damage is often present. In this work, we investigate whether classical isothermal unsaturated moisture transport can be used to simulate moisture ingress in damaged mortar and concrete and we compare the results of numerical simulations with experimental measurements of water sorption. The effect of hysteresis of moisture retention is also considered in the numerical simulations. The results indicate that the unsaturated moisture transport models well simulate early stages of moisture ingress at all damage levels, where capillary suction is the prominent mechanism. At later stages of moisture transport, where air diffusion and dissolution have a more significant contribution, simulations that consider moisture hysteresis compare most favorably with experimental results

Quantitative electrical imaging of three-dimensional moisture flow in cement-based materials

The presence of moisture significantly affects the mechanical, hydraulic, chemical, electrical, and thermal properties of cement-based and other porous materials, and therefore, methods for detecting and quantifying the moisture ingress in these materials are needed. Recent research studies have shown that the ingress of moisture in porous materials can be qualitatively imaged with Electrical Impedance Tomography (EIT) – an imaging modality which uses electrical measurements from object’s surface to reconstruct the electrical conductivity distribution inside the object. The aim of this study is to investigate whether EIT could image the three-dimensional volumetric moisture content within cement-based materials quantitatively. For this aim, we apply the so-called absolute imaging scheme to the EIT image reconstruction, and use an experimentally developed model for converting the electrical conductivity distribution to volumetric moisture content. The results of the experimental studies support the feasibility of EIT for quantitative imaging of three-dimensional moisture flows in cement-based materials

Fusing electrical and elasticity imaging

Abstract Electrical and elasticity imaging are promising modalities for a suite of different applications, including medical tomography, non-destructive testing and structural health monitoring. These emerging modalities are capable of providing remote, non-invasive and low-cost opportunities. Unfortunately, both modalities are severely ill-posed nonlinear inverse problems, susceptive to noise and modelling errors. Nevertheless, the ability to incorporate complimentary datasets obtained simultaneously offers mutually beneficial information. By fusing electrical and elastic modalities as a joint problem, we are afforded the possibility to stabilize the inversion process via the utilization of auxiliary information from both modalities as well as joint structural operators. In this study, we will discuss a possible approach to combine electrical and elasticity imaging in a joint reconstruction problem giving rise to novel multi-modality applications for use in both medical and structural engineering